【作者】 许进军；

【导师】 曾国熙；

【作者基本信息】 浙江大学 ， 岩土工程， 2001， 博士

【摘要】 本文用弹性动力学方程研究了无限长埋入桩的波动性状的若干问题。针对轴对称情况，推导了纵向模态的频率方程。频率方程代表了无量纲频率和无量纲波数之间的超越关系。频率方程的解为无究多个，并且形成无穷多支频散曲线（无量纲频率-无量纲波数曲线）。本文用数值方法计算了在软土与硬土中混凝土桩的前5支频散曲线。敏感性分析表明，无量纲波数实部与桩周土的剪切模量和密度无关，并与自由杆很一致。而波数虚部则，随着桩周土剪切模量与密度的增大而增大。 导波模态单位长度的衰减可以直接由波数虚部来代表。相速度和群速度随频率或波数而变化，这点与一维波动理论的假设相反。随着曲线分支阶次和频率的提高，导波模态的能量及位移分布曲线的起伏程度也相应增大。当无量纲频率低于2时，L（0，1）模态衰减最小，容易被激发，这点与实际中广泛采用的频响函数测试法（导纳法）相印证。当无量纲频率高于12时，模态L（0，2）衰减最小，其模态相对比较简单，这意味着这些模态在实际中也可能被激发。更多还原

【Abstract】 Guideci wave propagatjon in an infinitely long cylindrical pile embedded in soil is developed from dynamic equations ot?elasticity. Considering axisymmetric motion in the pile, the frequency equation for longitudinal modes is derived herein. The frequency equation represents a transcendental relationship between the non梔imensional frequency, Q, and non梔imensional wave number, Ja .The solution of the frequency equation is satisfied by an infinite number of modes that form branches in Q梸a plane. The first five branches of the longitudinal family of modes in a concrete pile embedded in sottjloose and hard dense soils were numerically evaluated respectively. Sensitivity analyses show that the real branches in the Q梸tplane are essentially independent of the shear modulus and density of the surrounding soil, and correspond closely to the branches of longitudinal modes in a free梥tanding?pile. However, the imaginary components of the branches in the Q梸~ plane are higher for soils with increased shear modulus and density. The attenuation of the longitudinal guided wave modes is represented directly by the imaginary part of the wave number, in nepers per length. The phase and group velocities vary with the frequency or wave number, contrary to the assumptions made in the theory of the one梔imensional approach. The power and displacement profiles of a given guided wave mode generally become more oscillatory as the order o~ the branch increases and as the frequency increases. For non梔imensional frequencies less than 2, the L (0, 1) modes display the lowest attenuation and are easily induced in a pile, as evidenced by the popularity of the impulse response test in practice. Modes on the L(0,2)hranch have the least attenuation compared to all other modes for non梔imensional frequencies above 12, and their relative simple mode shapes suggest that they are likely to be induced in practice.更多还原